Question: Two videos on viewtube.com were recently uploaded. One is a playful kitten video and the other is a laughing baby video. The kitten video had $10$ views by the end of the first minute after it was uploaded, and the cumulative number of views increases by $50$ views by the end of each additional minute. The baby video had $3$ views by the end of the first minute after it was uploaded, and the cumulative number of views increases by a factor of approximately $3.5$ by the end of each additional minute. By the end of which minute will the baby video's cumulative number of views first exceed the kitten video's cumulative number of views?
Notice that the kitten video's number of views grows linearly while the baby video's number of views grows exponentially. This means the baby video's number of views is bound to exceed the kitten video's number of views at some point. Let's start calculating each video's cumulative number of views to see when that happens. Minute Kitten video Baby video (Add $50$ each minute.) (Multiply by $3.5$ each minute.) $1$ $10$ $3$ $2$ $60$ $11$ $3$ $110$ $37$ $4$ $160$ $129$ $5$ $210$ $450$ In conclusion, the baby video's cumulative number of views will first exceed the kitten video's cumulative number of views in minute number $5$.